Statistical theory of multiple-site linear wall-adsorption capillary Chromatography

Based on the mass-balance principle, a particular diffusion equation to describe the movement of solute molecules in the stagnant layer of multiple-site solid surfaces is constructed. From the equation, the moments of residence time in a step on multiple-site surfaces are derived. Similarly, the moments in a step in the mobile phase are also derived from a diffusion-drift equation. According to the probability theory, there exists a general relationship between the moments of an elution curve and the moments in a step. Through this relationship, the expressions of the elution-curve moments are derived from the step moments. In this paper, the details related to multiple-site linear wall-adsorption capillary chromatography are described and added in the equations to determine the step moments. The resultant expressions of the elution-curve moments involve various factors, such as adsorption–desorption rate constants, equilibrium constants, axial and radial dispersions in the mobile phase. Afterwards, the moment expressions are used to analyze the peak tailing. The results show that a small quantity of sites with a slow desorption rate will lead to a large peak asymmetry.